Jubilant Republicans declared the US election race back on Thursday, calling Mitt Romney's resounding victory over Barack Obama in the first of the presidential debates a "game changer".

With just over a month left to the election, Republicans gleefully celebrated a rare win they are hoping will arrest Romney's campaign slump.

The Republican governor of New Jersey, Chris Christie, described Romney as having had a "game-changing debate" and expressed confidence he would be able to build on his victory.

A CNN flash poll of registered voters had 67% saying Romney had won it, while just 25% gave it to Obama.

Obama's team was engaged in a post-mortem into why the president had performed so badly in the debate, unable to cope with Romney's sustained aggression and appearing tired and disinterested.

Obama's chief strategist, David Axelrod, admitted the team was going to take "a hard look" at the president's performance, including whether he had failed to spend enough time in debate preparation.

He added the team will "make some judgments about where to draw the lines in these debates and how to use our time".

Both candidates hit the campaign trail on Thursday, Obama speaking at events in Colorado and Wisconsin, both swing states, and Romney in Colorado and another swing state, Virginia.

During a surprise appearance at the Colorado Conservative Political Action Conference meeting in Denver, Romney said the debate was a contrast of "two visions" telling the the crowd: "I saw the president's vision as trickle-down government and I don't think that's what America believes in. I see instead a prosperity that comes through freedom."

At a rally in Denver, Obama raised the theme the Democrats are going to push over the coming weeks: that Romney lied repeatedly during the debate. "You owe the American people the truth," he said.

Conservatives have gone overnight from viewing Romney as a lost cause to a candidate with at least a chance of the White House. Romney's team is hoping that his feisty performance in Denver will translate into rise in his poll figures and close the gap with Obama in swing states.

The Obama team expressed scepticism over whether there will be a shift in the polls, saying that while voters might have given the debate to Romney, that did not mean they intended to vote for him in the general election.

Romney has been struggling for months, with one setback after another, unable to get ahead of Obama. In spite of the boost to his campaign from the debate, Romney still faces an extremely tough task in turning around the swing states.

However, his campaign is almost certain to receive another boost on Friday when the monthly jobs figures are released and these are expected to show little change from unemployment that has been hovering around 8% this year.

As both campaigns anxiously awaited the first batch of polls, Romney appeared to have achieved at least one initial reward: donors who had been threatening to switch their funds from Romney, giving up on him in favour of channelling money to Republicans in winnable Congressional races, hoping to take the Senate. Andrea Saul, Romney's press secretary, tweeted that after the debate the Republican challenger received more than two donations every second.

Erick Erickson, conservative editor of the widely-read Red State blog, wrote in a tweet: "Been on a call with some Romney donors who tonight abandon the idea of moving their money to congressional races. They'll stay with him."

Reflecting the sense of triumphalism among Republicans, Erickson also tweeted that the Democrats might be better putting up an empty chair instead of Obama next time and asking who would notice, a reference to Clint Eastwood's performance at the Republican convention.

James Carville, one of Bill Clinton's strategist, conceded on CNN that Obama had been off his game and could not cope with Romney's aggression. "Romney came in with a chainsaw. He's trying to talk to a chainsaw," Carville said.

Romney's win increases the interest in next week's vice-presidential debate between Joe Biden and his Republican opponent Paul Ryan. The Republicans will be keen to keep the momentum building with another win before Obama and Romney square off again, in New York state, on 16 October.